I will go with TG2 and IKnowNot on this one. Your extension cable is defective so send it back.

The acid test is that the cable was supplied with the Alfa range extender and doesn't work with it?............... that means that it is defective. The Afa works otherwise, as does the USB memory stick, so those units must be OK? I am afraid that only leaves the cable itself as the culprit.

USB basically performs a dual function: power and signal. Your USB memory stick shouldn't use much more power than the mouse, although the connectivity (signal) is much less sophisticated for the mouse, which is probably why it works.

Simple view: "I bought an Alfa with a lead, it doesn't work, nor does it with a memeory stick, yet both devices work otherwise...............send me a new cable like yesterday"

DO NOT mention that it works with a mouse.............did you buy it for that?